Maybe this is normal, maybe not. I just never noticed it until I tried long exposures this month.

I noticed there are probably 20+ (red, purple, white) dots that will show up in the same spot every time I do a long exposure with a dark background. The longer the exposure/higher ISO, the brighter they become. It happens with every lens, so I think it's the sensor. To test it, I decided to place the lens cap on for total darkness, and shoot varying exposures.
1 sec @ 100 ISO no issue.
2.5 sec @ 100 ISO very faint
30 sec @ 100 ISO obvious
30 sec @ 1600 ISO more obvious
Enabling "Long Exposure Noise Reduction" completely eliminated it @ 30 sec/100 ISO.

Thanks for the feedback. Much appreciated. I figured it was normal, but a little voice in the back of my head was nagging me, lol. I tried the 30 sec 100 ISO test with a friend's Nikon D40x and it had no hot pixels, which made me think my camera was defective. But the Nikon may have had some auto-processing that automaticly reduces long exposure noise.

By the way, this is AFTER my father (who is a broadcast engineer for an NBC affiliate) who said this was completely normal, lol. I'm just being paranoid at this point. Thanks.

Yup, perfectly normal, although some may be better or worse than others. As you noted, cameras do provide the "long duration exposure noise removal" function to take care of it for you, at the cost of increasing the amount of time taken per exposure.

On more modern Canons, the 7D at 30 seconds has the odd spot of colour noise, whereas on the 450D I find you get a lot of red spots.

Press the Menu button, and find Manual Sensor Cleaning. Run the Manual Sensor Cleaning process for about thirty seconds, and then cancel it. I'd do this in a dimly lit room to prevent any chance, however small, of light entering via the viewfinder.

Put the lens back on the camera and try some test shots

This was reputed to work with the 40D although it is undocumented. It may not work with the Rebel XS/1000D but it can't do any harm to give it a try. If it does work then please let us know.

I tried your advice. I did a manual sensor clean for roughly 30 sec and shut the power off (I could not find another method to cancel it) and did a 30 sec 100 ISO test with lens cap on. It is still the same, but I thank you for the post and idea. I'm not worried about it, but thanks for the reply.

The process Bob described works for temporary "hot" pixels. I've used that before on the 50D but not needed it on other cameras. That may only really fix bright pixels that appear when the exposure isn't really long.